Stationary Discounted and Ergodic Mean Field Games of Singular Control

Cao, Haoyang; Dianetti, Jodi; Ferrari, Giorgio

doi:10.48550/arxiv.2105.07213

Cited by 4 publications

(6 citation statements)

References 54 publications

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“…By employing, respectively, the connection to problems of optimal stopping and PDE methods, the structure of the mean-field equilibrium as well as its connection to Nash equilibria for the corresponding N -player stochastic differential games is derived. Finally, [16] and [15] study stationary MFGs, i.e. games in which the interaction comes through the stationary distribution of the population of players.…”

Section: 2mentioning

confidence: 99%

“…games in which the interaction comes through the stationary distribution of the population of players. [15] considers ergodic and discounted performance criteria, and studies the relation across the corresponding equilibria; in [16] the representative player can employ two-sided controls in order to adjust a geometric dynamics and optimize a certain discounted payoff. It is worth noting that none of the previous contributions allows for the presence of common noise, which we can instead treat in our analysis.…”

Section: 2mentioning

confidence: 99%

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A unifying framework for submodular mean field games

Dianetti¹,

Ferrari²,

Fischer³

et al. 2022

Preprint

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We provide an abstract framework for submodular mean field games and identify verifiable sufficient conditions that allow to prove existence and approximation of strong mean field equilibria in models where data may not be continuous with respect to the measure parameter and common noise is allowed. The setting is general enough to encompass qualitatively different problems, such as mean field games for discrete time finite space Markov chains, singularly controlled and reflected diffusions, and mean field games of optimal timing. Our analysis hinges on Tarski's fixed point theorem, along with technical results on lattices of flows of probability and sub-probability measures.

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Section: 2mentioning

confidence: 99%

Section: 2mentioning

confidence: 99%

A unifying framework for submodular mean field games

Dianetti¹,

Ferrari²,

Fischer³

et al. 2022

Preprint

Self Cite

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“…In the stationary mean-field regime [31], [32], [35], the following additional assumptions are made: -Time homogeneous strategy: All IoT devices follow a time-homogeneous power allocation strategy 𝑝 𝑡 = 𝑝 : Ω → [0, 𝑃 𝑚𝑎𝑥 ].…”

Section: B Stationary Regimementioning

confidence: 99%

“…This approximation, however, is only significant if the associated approximation error is small. It has been shown that under appropriate conditions, the mean-field regime realizes an 𝜖-Nash equilibrium for the dynamic differential game, with 𝜖 converging to zero as the number of players goes to infinity [35].…”

Section: B Stationary Regimementioning

confidence: 99%

Traffic-Aware Mean-Field Power Allocation for Ultra-Dense NB-IoT Networks

Nadif¹,

Sabir²,

Elbiaze³

et al. 2022

Preprint

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The Narrowband Internet of Things (NB-IoT) is a cellular technology introduced by the Third-Generation Partnership Project (3GPP) to provide connectivity to a large number of low-cost IoT devices with strict energy consumption limitations. However, in an ultra-dense small cell network employing NB-IoT technology, inter-cell interference can be a problem, raising serious concerns regarding the performance of NB-IoT, particularly in uplink transmission. Thus, a power allocation method must be established to analyze uplink performance, control and predict inter-cell interference, and avoid excessive energy waste during transmission. Unfortunately, standard power allocation techniques become inappropriate as their computational complexity grows in an ultra-dense environment. Furthermore, the performance of NB-IoT is strongly dependent on the traffic generated by IoT devices. In order to tackle these challenges, we provide a consistent and distributed uplink power allocation solution under spatiotemporal fluctuation incorporating NB-IoT features such as the number of repetitions and the data rate, as well as the IoT device's energy budget, packet size, and traffic intensity, by leveraging stochastic geometry analysis and Mean-Field Game (MFG) theory. The effectiveness of our approach is illustrated via extensive numerical analysis, and many insightful discussions are presented.

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“…Both papers do not consider the vanishing discount approach which we do here. The recent paper [5] considers the vanishing discount approach, but in a continuous-time setting and for a game.…”

Section: Introductionmentioning

confidence: 99%

Mean Field Markov Decision Processes

Bäuerle¹

2021

Preprint

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We consider mean-field control problems in discrete time with discounted reward, infinite time horizon and compact state and action space. The existence of optimal policies is shown and the limiting mean-field problem is derived when the number of individuals tends to infinity. Moreover, we consider the average reward problem and show that the optimal policy in this mean-field limit is ε-optimal for the discounted problem if the number of individuals is large and the discount factor close to one. This result is very helpful, because it turns out that in the special case when the reward does only depend on the distribution of the individuals, we obtain a very interesting subclass of problems where an average reward optimal policy can be obtained by first computing an optimal measure from a static optimization problem and then achieving it with Markov Chain Monte Carlo methods. We give two applications: Avoiding congestion an a graph and optimal positioning on a market place which we solve explicitly.

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Stationary Discounted and Ergodic Mean Field Games of Singular Control

Cited by 4 publications

References 54 publications

A unifying framework for submodular mean field games

A unifying framework for submodular mean field games

Traffic-Aware Mean-Field Power Allocation for Ultra-Dense NB-IoT Networks

Mean Field Markov Decision Processes

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